diff --git a/client.go b/client.go
index edd9368b..e7ff786a 100644
--- a/client.go
+++ b/client.go
@@ -185,9 +185,20 @@ func (c *Client) exchange(m *Msg, co *Conn) (r *Msg, rtt time.Duration, err erro
 	}
 
 	co.SetReadDeadline(time.Now().Add(c.getTimeoutForRequest(c.readTimeout())))
-	r, err = co.ReadMsg()
-	if err == nil && r.Id != m.Id {
-		err = ErrId
+	if _, ok := co.Conn.(net.PacketConn); ok {
+		for {
+			r, err = co.ReadMsg()
+			// Ignore replies with mismatched IDs because they might be
+			// responses to earlier queries that timed out.
+			if err != nil || r.Id == m.Id {
+				break
+			}
+		}
+	} else {
+		r, err = co.ReadMsg()
+		if err == nil && r.Id != m.Id {
+			err = ErrId
+		}
 	}
 	rtt = time.Since(t)
 	return r, rtt, err
diff --git a/client_test.go b/client_test.go
index b75d946c..11c8469d 100644
--- a/client_test.go
+++ b/client_test.go
@@ -3,6 +3,7 @@ package dns
 import (
 	"context"
 	"crypto/tls"
+	"errors"
 	"fmt"
 	"net"
 	"strconv"
@@ -162,6 +163,12 @@ func TestClientTLSSyncV4(t *testing.T) {
 	}
 }
 
+func isNetworkTimeout(err error) bool {
+	// TODO: when Go 1.14 support is dropped, do this: https://golang.org/doc/go1.15#net
+	var netError net.Error
+	return errors.As(err, &netError) && netError.Timeout()
+}
+
 func TestClientSyncBadID(t *testing.T) {
 	HandleFunc("miek.nl.", HelloServerBadID)
 	defer HandleRemove("miek.nl.")
@@ -175,12 +182,66 @@ func TestClientSyncBadID(t *testing.T) {
 	m := new(Msg)
 	m.SetQuestion("miek.nl.", TypeSOA)
 
-	c := new(Client)
-	if _, _, err := c.Exchange(m, addrstr); err != ErrId {
-		t.Errorf("did not find a bad Id")
+	c := &Client{
+		Timeout: 50 * time.Millisecond,
+	}
+	if _, _, err := c.Exchange(m, addrstr); err == nil || !isNetworkTimeout(err) {
+		t.Errorf("query did not time out")
 	}
 	// And now with plain Exchange().
-	if _, err := Exchange(m, addrstr); err != ErrId {
+	if _, err = Exchange(m, addrstr); err == nil || !isNetworkTimeout(err) {
+		t.Errorf("query did not time out")
+	}
+}
+
+func TestClientSyncBadThenGoodID(t *testing.T) {
+	HandleFunc("miek.nl.", HelloServerBadThenGoodID)
+	defer HandleRemove("miek.nl.")
+
+	s, addrstr, err := RunLocalUDPServer(":0")
+	if err != nil {
+		t.Fatalf("unable to run test server: %v", err)
+	}
+	defer s.Shutdown()
+
+	m := new(Msg)
+	m.SetQuestion("miek.nl.", TypeSOA)
+
+	c := new(Client)
+	r, _, err := c.Exchange(m, addrstr)
+	if err != nil {
+		t.Errorf("failed to exchange: %v", err)
+	}
+	if r.Id != m.Id {
+		t.Errorf("failed to get response with expected Id")
+	}
+	// And now with plain Exchange().
+	r, err = Exchange(m, addrstr)
+	if err != nil {
+		t.Errorf("failed to exchange: %v", err)
+	}
+	if r.Id != m.Id {
+		t.Errorf("failed to get response with expected Id")
+	}
+}
+
+func TestClientSyncTCPBadID(t *testing.T) {
+	HandleFunc("miek.nl.", HelloServerBadID)
+	defer HandleRemove("miek.nl.")
+
+	s, addrstr, err := RunLocalTCPServer(":0")
+	if err != nil {
+		t.Fatalf("unable to run test server: %v", err)
+	}
+	defer s.Shutdown()
+
+	m := new(Msg)
+	m.SetQuestion("miek.nl.", TypeSOA)
+
+	c := &Client{
+		Net: "tcp",
+	}
+	if _, _, err := c.Exchange(m, addrstr); err != ErrId {
 		t.Errorf("did not find a bad Id")
 	}
 }
diff --git a/server_test.go b/server_test.go
index 864b52f5..c76c7a77 100644
--- a/server_test.go
+++ b/server_test.go
@@ -35,6 +35,19 @@ func HelloServerBadID(w ResponseWriter, req *Msg) {
 	w.WriteMsg(m)
 }
 
+func HelloServerBadThenGoodID(w ResponseWriter, req *Msg) {
+	m := new(Msg)
+	m.SetReply(req)
+	m.Id++
+
+	m.Extra = make([]RR, 1)
+	m.Extra[0] = &TXT{Hdr: RR_Header{Name: m.Question[0].Name, Rrtype: TypeTXT, Class: ClassINET, Ttl: 0}, Txt: []string{"Hello world"}}
+	w.WriteMsg(m)
+
+	m.Id--
+	w.WriteMsg(m)
+}
+
 func HelloServerEchoAddrPort(w ResponseWriter, req *Msg) {
 	m := new(Msg)
 	m.SetReply(req)